# Compositeness of quarks and leptons

1. Feb 16, 2013

### welatiger

Is the discovery of Higgs boson contradict the Compositeness model and the preon existence ???!!!

2. Feb 16, 2013

### mathman

The Higgs boson was considered part of the Standard Model, so nothing has changed.

Note: Your sentence is unclear - could you define the terms?

3. Feb 17, 2013

### welatiger

You Know that in the compositeness model, the spontaneous symmetry breaking is due to the preon but not the Higgs boson.

4. Feb 17, 2013

### mathman

To be honest, I never heard of the compositeness model.

5. Feb 17, 2013

### arivero

Do you mean, you have never heard of _any_ compositeness model???? Fascinating.

6. Feb 18, 2013

### welatiger

Dear all
The compositness model was first proposed by A.Salam 1970, mainly due to the hairechary problem, you can read about it in wiki pages.

7. Feb 18, 2013

### Devils

To move this discussion along:
http://en.wikipedia.org/wiki/Preon
"In particle physics, preons are postulated "point-like" particles, conceived to be subcomponents of quarks and leptons.[1] The word was coined by Jogesh Pati and Abdus Salam in 1974. Interest in preon models peaked in the 1980s but has slowed as the Standard Model of particle physics continues to describe the physics mostly successfully, and no direct experimental evidence for lepton and quark compositeness has been found, although in the hadronic sector there are some intriguing open questions and some effects considered as anomalies within the Standard Model."

8. Feb 18, 2013

### mathman

Devils gave an answer to my question. The assertion that leptons or quarks are composite is so far completely unproven.

9. Feb 18, 2013

### arivero

Perhaps the point is if there is someone here in the forum.who is interested on composites. If nobody can comment beyond the wikipedia, it is probably not worth to raise the topic here.

10. Feb 19, 2013

### mathman

It is not just Wikipedia. It is the overwhelming consensus of the physics community that there is no evidence for compositeness of leptons and quarks.

Aside: spellcheck doesn't think "compositeness" is a word.

11. Feb 19, 2013

### arivero

There is a consensus on the no evidence of substructure. I fact even my esoteric sBootstrap is in the consensus, as it only ask for compositeliness (hey, that is worse!) for the scalar partners of the fermions in a susy theory.

But generically, I wonder if absence of substructure (ie, to be point-like in 4D) implies absence of compositeness. I am not sure if the fermionic states of a superstring theory are pointlike or not. And even if they are not pointlike, an open string in a 4D brane should be.

12. Feb 20, 2013

### DimReg

I feel like I should point this out:

If a particle is composite, it has to have a finite radius (because at a small enough scale it is more than one particle). But we have experimental bounds on the radius of fundamental particles (I'm not sure if we have done this for all or just some). These bounds are very small, the radius of these particles are tiny. In order to have a composite particle with a very short radius, you need a very strong interaction, which raises the potential energy of the composite particle. But raising the energy like this also increases the mass of the composite particle.

So right now to make composite particles have a radius and mass consistent with what we have observed, is very difficult. As far as I know this is the main reason that preon models (and general composite models) are disfavored.

13. Feb 20, 2013

### arivero

I am not sure, I have never seen a proof, besides the *classical* intuition that you mention.

Particularly, what does it happen with the fermionic states of the superstring? In the worldsheet, is there some rule telling that the bosonic coordinates X_mu, which are the actual location of the string in space time, need to be as a particle of finite radius?

14. Feb 20, 2013

### DimReg

The finite radius of a string is a completely different thing. The string is not taken to be a composite particle, as far as I know.

A composite particle is a bound state of two particles, at least as far as they are usually discussed. In that case, there is ALWAYS a finite radius, there is the average separation of the particles from each other. If this distance were 0, it would imply an enormous binding energy, which most likely would be too large (creates a black hole).

I'm not sure how I would rigorously prove this for a general case. However, as a model you can use the infinite spherical well potential, so inside the radius the particle is free to move but a very strong restoring force holds the particle in if it tries to leave that radius (also, you do the usual trick of reducing a two body problem to a one body problem). The ground state energy (actually all energy levels) goes as r^-2, where r is the radius of the well. Clearly this diverges when r goes to 0.

For string theory, the finite size of the string is ideal because it "spreads out" the gravitational interaction, making the perturbation series renormalizable. This is why it's considered a promising candidate for a quantum theory of gravity. If the string wasn't extended, it wouldn't be a good theory of gravity. But most importantly, there isn't some derived rule that says that the string has to be an extended object, it is the postulated form a particle takes, and thus by construction the string in string theory is extended.

15. Feb 20, 2013

### arivero

Fine example, but that is not all the history. For 1D potentials, we are granted that there is always at least a bound state inside a well, so what happens in the limit of "point-supported potentials" is a single state, if the potential is only supported in one point. Actually the classification of the possible states is equal to the possible boundary conditions, some of then can be produced as limits of potentials going to dirac-delta shapes, some others have other origins. A classic textbook on the topic, by the way, is wrong about the naming of the classification.

For 3D well, the case is as you describe, but Gosdzinsky-Tarrach and and Manuel-Tarrach found a way to "renormalise" the interaction, again producing a single bound state in the limit of point-like potential.

So I had never though of it, but these interactions could be described, via the two body to one body reduction, as examples of composite states with point-like properties.

The "construction" is that a world-sheet has a bosonic field $X_\mu(\sigma)$ with sigma taking values from a one-dimensional segment, but it does not tell that the projection in the target space, the one where the X maps to, is an extended object. I think that it is clear that for bosonic states it is, with the restriction that it could be "pointlike" in some subset of the coordinates (a "D-brane"). And for fermionic states, I have never seen a clear discussion.

16. Feb 21, 2013

### lpetrich

Looking at history, putatively elementary entities were discovered to be composite when one pounds them hard enough -- they start to break apart. That was true of atoms, that was true of nuclei, and that was true of hadrons.

But that is not true of either quarks or leptons, to within experimental limits, despite pounding them with much more energy than their rest masses.

You can find some tests of compositeness at Particle Data Group:
"Summary Data" > "Searches (Monopoles, SUSY, Technicolor, Compositeness, ...)"
"Reviews, Tables, Plots" > "Searches for Quark and Lepton Compositeness"

These links give a thumbnail history:
Deep Inelastic Scattering of Electrons
Survey of Scattering Investigations

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Let's see what the binding energies look like for atoms, nuclei, and hadrons.

For atoms, one can add up the ionization potentials, the energy necessary to remove each electron. Ionization energies of the elements (data page) - Wikipedia has complete ones up to copper (Z = 29). I find a good fit to Z2.4 * 14 eV.

However, even these elements' innermost electrons are nonrelativistic, so this fit may not carry over very well to the heaviest elements. But using it for the heaviest element with a cosmological mean life, uranium (Z = 92), gives 0.72 MeV, a little more than the rest mass of an electron. The total rest masses of the electrons is 47 MeV, and the total rest mass of a uranium-238 atom is 222 GeV. That gives ratios 0.015 for the electrons and 3.2*10^(-6) for the entire atom.

For hydrogen-1, however, the ratios are 2.7*10^(-5) and 1.4*10^(-8).

Turning to nuclei, let us check on Nuclear binding energy - Wikipedia. The lowest mass per nucleon is for iron-56. It has a binding energy of 8.79 MeV per nucleon, or 0.0094 relative to the unbound protons and neutrons.

Hadron binding energy is poorly defined, since quarks can't be free. But for light hadrons, interaction energies are close to the valence quarks' kinetic energies, so we can say ~ 1 here. However, due to a quirk of QCD called chiral symmetry breaking, pions' masses are about sqrt(EQCD{/sub]*(mu+md)) -- they would be massless if the up and down quarks were massless. Is that due to cancellation?

But let's consider the experimental limits' ratios to the rest masses of the particles studied.

For electrons, the clearest results are from LEP, which went up to 104.4 GeV. Electrons' behavior was in close agreement with the Standard Model up to that energy, meaning that electrons' compositeness energy scale has to be at least that energy.

For its just-completed run, the LHC may be able to get results for energies up to about 1 TeV, at least for the up and down quarks.

So rest mass / compositeness scale:
LEP electrons: 5*10^(-6)
LEP up/down: 3*10^(-5)
LHC electrons: 5*10^(-7)
LHC up/down: 3*10^(-6)

(up and down quark masses ~ 3 MeV)

If the electron's compositeness scale is 500 GeV, then if it gets its mass in pion-like fashion, its constituents must have res masses of about 0.5 eV. This requires something like color confinement, because no such free particles are known to exist.